I will talk on the dissipationless current driven by the
Berry phase curvature in the momentum space. It is defined by the
connection of the Bloch wavefunctions, and ubiquitous in
solids. Also the interesting feature of this Berry phase is
that the gauge field can have the "magnetic monopoles"
corresponding to the band crossing in momentum space,
in sharp contrast to the real space magnetic field.
The talk will cover the anomalous Hall effect in ferromagnets,
spin chirality driven Hall effect, spin current generation by electric
field in semiconductors, and spin quantum Hall effect.